# How do you simplify #cos^-1(sqrt2/2)#?

##### 2 Answers

Aug 3, 2017

#### Explanation:

This value is actually a standard value in disguise. Surds are often removed from the denominator of a fraction by multiplying top and bottom by the surd in question. We can do exactly the same thing to put the surd back in the denominator:

Maybe you recognise the value now.

What value of theta gives this value? It is one that should be memorised if you have exams on trigonometry.

Writing this another way, we have:

Aug 3, 2017

#### Explanation:

Trig table and unit circle give -->

or, using co-terminal arcs: